A length of pipe generally connects a hot water source and a faucet. As hot water stands in this pipe, it cools down. This occurs whether or not the pipe is insulated, the only difference being the rate of cooling. Consequently, when one turns on a faucet, there is a delay associated with delivery of hot water. This delay arises because the cold water in the pipe must be delivered out the faucet so that warm water from the hot water source can replace it.
The length of this delay is governed in part by the volume of the pipe. In the case of a half-inch pipe extending about 50 feet under normal residential water pressure, the delay is on the order of 25-30 seconds before water exiting the pipe is at a temperature that corresponds to that of the hot water source.
The delay associated with having to run the water before receiving hot water wastes water since a considerable volume is discarded. Additionally, the delay is annoying to those with an impatient disposition.